Tiny Tate Bilinear Pairing Core
Category: Arithmetic Core
Created: April 19, 2012
Updated: January 27, 2020
Other project properties
Development Status: Stable
Additional info: Design done, Specification done
WishBone compliant: No
WishBone version: n/a
Tiny Tate Bilinear Pairing core is for calculating Tate bilinear pairing.
In fact it is a special type of Tate bilinear pairing called reduced $\eta_T$ pairing.
Its features are:
* super-singular elliptic curve E:y^2=x^3-x+1
* the field is the Galois field GF(3^m),m=97 or 593
* the irreducible polynomial is x^97+x^12+2 or x^593+x^112+2
* the group size is 151 bits or 911 bits
* vendor independent code
* very low hardware cost (≤0.2 US dollar) if m=97
* released under Apache License v2.0
Document & Specification
Specification (low secure level, 151 bits group size)
Specification (high secure level, 911 bits group size)
The reduced $η_T$ pairing is introduced by Barreto et.al.
There are at least two related nice papers:
 P.Barreto, S.Galbraith, C.O hEigeartaigh, and M.Scott. Efficient pairing computation on supersingular abelian varieties. in
Designs, Codes and Cryptography. Springer Netherlands, Mar. 2007, vol. 42(3), pp. 239–271.
 J.Beuchat, N.Brisebarre, J.Detrey, E.Okamoto, M.Shirase, and T.Takagi. Algorithms and arithmetic operators for computing the η_T pairing in characteristic three. in IEEE Transactions on Computers, Special Section on Special-Purpose Hardware for Cryptography and Cryptanalysis, 57(11):1454-1468, 2008.
Synthesis results (ISE)
Low secure level core
|Device:||Xilinx Spartan 3 XC3S200-5PQ208|
|Number of Slice Flip Flops:||1,319|
|Number of 4 input LUTs:||3,028|
|Number of occupied Slices:||1,730|
|Number of bonded IOBs:||15|
Synthesis results (Quartus)
Low secure level core
|Device:||Altera Cyclone II EP2C20F484C7|
|Total logic elements:||3,637|
|Dedicated logic registers:||1,310|
|Total memory bits:||25,984|
The low secure level core computes one Tate pairing in 1.05 milliseconds if with a 50MHz clock.
The high secure level core computes one Tate pairing in 20.0 milliseconds if with a 50MHz clock.
Xilinx Spartan 3 XC3S200 FPGA is enough for the low secure level core.
The price of that FPGA is less than 0.2 USA dollar per piece in 2012.
Compared to "Tate Bilinear Pairing core"
|Tiny Tate Bilinear Pairing core||Tate Bilinear Pairing core|
|Device:||Xilinx Spartan 3 XC3S200||Xilinx Virtex 4 XC4VLX200|
|Number of Slice Flip Flops:||1,319||31,383|
|Number of 4 input LUTs:||3,028||47,083|
|Number of occupied Slices:||1,730||30,149|
|Computation time:||1.02ms||0.76 ms|
This core follows the idea in the academic paper of Mr.Beuchat et.al.
This core uses 20% less FPGA slices, 50% less RAM memory than Mr.Beuchat et.al.
But this core is slower than Mr.Beuchat et.al.